Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options.

We know that the radius of a nucleus is given by $$R = R_0 A^{1/3}$$, where $$R_0 \approx 1.2 \times 10^{-15}$$ m is a constant and $$A$$ is the mass number. The volume of the nucleus is then $$V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi R_0^3 A$$. Since $$\frac{4}{3}\pi R_0^3$$ is a constant, we see that the volume is directly proportional to the mass number $$A$$. Hence, statement (A) is correct and statement (B) is incorrect.

Now, the mass of the nucleus is approximately $$M = A \cdot m_u$$, where $$m_u$$ is the atomic mass unit. The density of the nucleus is $$\rho = \frac{M}{V} = \frac{A \cdot m_u}{\frac{4}{3}\pi R_0^3 A} = \frac{m_u}{\frac{4}{3}\pi R_0^3}$$. We see that the mass number $$A$$ cancels out completely, so the nuclear density is a constant, independent of the mass number. Hence, statement (E) is correct, while statements (C) and (D) are incorrect.

Hence, the correct answer is Option B.